3 Answers
3

Since geshem changing to gashem is dependent on whether the word comes at the completion of a phrase (esnachta or sof pasuk), the real question is:

Is the ability to make rain a praise in itself (ending the phrase- hagashem), or is it only a praise if it is used to sustain life and must be followed by mechalkel chaim b'chesed (hageshem)

There are many in each camp. Interestingly, even though Rav Moshe writes hagashem, the sefer Tefila K'hilchasa quote a pamphlet (Mechalkel Chaim) which claims much support for hageshem and claims that Rav Moshe retracted.

My sefer doesn't say. I tried googling to no avail, but came up with this interesting piece on why the siddurim that have hageshem have morid hatal with a kamatz: webcache.googleusercontent.com/…
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YDKOct 3 '10 at 22:15

Interesting point. A blogger on the site I linked to above wanted to say the opposite since we don't continue with mechalkel chaim, but you sound more correct since we continue the sentence liklala... It's hard to tell what is put in by the publishers and what is based on halachik dikduk.
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YDKDec 30 '10 at 15:46

Actually the sefer you are refering to is Birchos HaChaim. It is available on Otzar HaChochma.
Based on what I have read so far, the correct reading would be haGESHEM.
(I have not found yet where he says that Rav Moshe retracted, but I have only gone through half of the 97 pages).
The nusach of haGASHEM seems to have been put in by a maskil...
He also discusses if haTal should be with a kametz or a patach.
Check the sefer for a full explanation.

Moshe Flohr, Welcome to mi.yodeya, and thanks very much for the additional information! We'd love to have you as a fully-registered member, which you can accomplish by clicking "register," above.
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Isaac MosesOct 18 '10 at 0:28

See Shu”t Teshuvos V’Hanhagos vol. 1, 81 w& vol 2, 58 who cites like you claim that the pronouncing of the word as “Gashem” was introduced by Maskilim, Rav Sternbuch puts this notion to rest, quoting earlier sources that also said “Gashem” (even though he personally argues).
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cmbOct 16 '12 at 9:31

also i would not rely lmaaseh on the tefillah kehilchasa's claims that rav moshe retracted. if he would have, it would be listed in more reliable sources. many others including rav elyashiv said gashem as well. I think he is confusing it with rav shlomo zalman auerbach who is quoted in halichos shlomo as retracting after reading birchos chaim.
the tefillah khilchasa also claims that the gr"a said geshem - and that the steipler said gashem - both the exact opposite of every other source.